The Siegel – Bruno Linearization Theorem

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI:10.1134/S1560354723040147

Patrick Bernard

引用次数: 0

Abstract

The purpose of this paper is a pedagogical one. We provide a short and self-contained account of Siegel’s theorem, as improved by Bruno, which states that a holomorphic map of the complex plane can be locally linearized near a fixed point under certain conditions on the multiplier. The main proof is adapted from Bruno’s work.

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Siegel–Bruno线性化定理

本文的目的是为了教学。我们对Bruno改进的Siegel定理进行了简短而独立的解释，该定理指出复平面的全纯映射可以在乘法器上的某些条件下在不动点附近局部线性化。主要证据改编自布鲁诺的作品。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.